On the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids

作     者：David Hoff Konstantina Trivisa 

作者机构：Department of MathematicsIndiana University BloomingtonIN 47405-4301USADepartment of Mathematics University of MarylandCollege Park MD 20742-4015USA 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2002年第18卷第1期

页      面：15-36页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported in part by the National Science Foundation under Grants DMS-9971793  INT-9987378 and INT-9726215.Supported in part by the National Science Foundation under Grant DMS-9703703.Supported in part by the National Science Foundation under Grants 

主　　题：Global discontinuous solutions discontinuous initial data large oscillation evolution of large jump discontinuities asymptotic behavior combustion Navier-Stokes equations difference approximations energy estimates total variation estim 

摘      要：We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, and large-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations with constant adiabatic exponent γ and specific heat Cv. Our approach for the existence and regularity is to combine the difference approximation techniques with the energy methods, total variation estimates, and weak convergence arguments to deal with large jump discontinuities; and for large-time behavior is an a posteriori argument directly from the weak form of the equations. The approach and ideas we develop here can be applied to solving a more complicated model where γand cv vary as the phase changes; and we then describe this model in detail and contrast the results on the asymptotic behavior of the solutions of these two different models. We also discuss other physical models describing dynamic combustion.